First, if you have a "block diagonal" matrix as in your example, the eigenvalues of the matrix are the combined eigenvalues of the smaller blocks on the diagonal. So, yes, in the case of the $4 \times 4$ matrix, the eigenvalues are just those of the two $2 \times 2$ blocks on its diagonal (repeated according to multiplicity).
Second, swapping two rows (or two columns, resp.) does not preserve eigenvalues and has a somewhat unpredictable effect on the eigenvalues. However if you swap both a pair of rows and the corresponding pair of columns, this is a similarity tranformation and preserves the eigenvalues (according to multiplicity).
